Comparison of Austenite Decomposition Models During Finite Element Simulation of Water Quenching and Air Cooling of AISI 4140 Steel

An indigenous, non-linear, and coupled finite element (FE) program has been developed to predict the temperature field and phase evolution during heat treatment of steels. The diffusional transformations during continuous cooling of steels were modeled using Johnson–Mehl–Avrami–Komogorov equation, and the non-diffusion transformation was modeled using Koistinen–Marburger equation. Cylindrical quench probes made of AISI 4140 steel of 20-mm diameter and 50-mm long were heated to 1123 K (850 °C), quenched in water, and cooled in air. The temperature history during continuous cooling was recorded at the selected interior locations of the quench probes. The probes were then sectioned at the mid plane and resultant microstructures were observed. The process of water quenching and air cooling of AISI 4140 steel probes was simulated with the heat flux boundary condition in the FE program. The heat flux for air cooling process was calculated through the inverse heat conduction method using the cooling curve measured during air cooling of a stainless steel 304L probe as an input. The heat flux for the water quenching process was calculated from a surface heat flux model proposed for quenching simulations. The isothermal transformation start and finish times of different phases were taken from the published TTT data and were also calculated using Kirkaldy model and Li model and used in the FE program. The simulated cooling curves and phases using the published TTT data had a good agreement with the experimentally measured values. The computation results revealed that the use of published TTT data was more reliable in predicting the phase transformation during heat treatment of low alloy steels than the use of the Kirkaldy or Li model.     

Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars

A mathematical model, based on the finite-element technique and incorporating thermo-elasto-plastic behavior during the water spray quenching of steel, has been developed. In the model, the kinetics of diffusion-dependent phase transformation and martensitic transformation have been coupled with the transient heat flow to predict the microstructural evolution of the steel. Furthermore, an elasto-plastic constitutive relation has been applied to calculate internal stresses resulting from phase changes as well as temperature variation. The computer code has been verified for internal consistency with previously published results for pure iron bars. The model has been applied to the water spray quenching of two grades of steel bars, 1035 carbon and nickel-chromium alloyed steel; the calculated temperature, hardness, distortion, and residual stresses in the bars agreed well with experimental measurements. The results show that the phase changes occurring during this process affect the internal stresses significantly and must be included in the thermomechanical model. Y. NAGASAKA, formerly Visiting Research Engineer with the University of British Columbia. S.E. CHIDIAC, formerly Research Associate with the University of British Columbia.     

重轨轨头淬火应力场的计算机模拟

利用有限元法研究了重轨轨头在淬火过程中的应力场分布。模拟计算的过程中利用等效热容法处理相变潜热对温度场的影响,用等效线膨胀系数法处理相变引起的组织应力,同时考虑了材料的非线性参数对温度场的影响。研究结果表明温度的模拟结果与实测结果吻合较好,喷风淬火可以产生较小的残余热应力,避免了钢轨的变形和开裂。     

Q&P钢在冷却过程中铁素体的相变规律

 为了研究冷却过程中Q&P钢(quenching and partition steel)铁素体的相变规律,在热膨胀仪上以846 ℃均热200 s为冷却的初始条件,检测了成分(质量分数)为0.2%C、1.25%Si、2.0%Mn的Q&P钢在不同冷却速率下铁素体的相变热膨胀数据,应用杠杆定律将数据处理为相变规律与温度的关系,通过光学显微镜检测热处理后金相中的铁素体相体积分数和铁素体晶粒尺寸,得出了饱和位置形核条件下铁素体的形核率,基于混合控制模型得出了铁素体相变的相界迁移速率。结合相变开始温度,利用混合控制模型计算了相变结束温度和铁素体晶粒尺寸在相变过程中的演变规律,铁素体晶粒尺寸计算值与实测值吻合程度较高,相变结束温度的计算值与实测值的误差在±15 ℃以内,所获得的铁素体相变规律可以用于控制Q&P钢在冷却过程中的铁素体相变体积分数。     

A Finite Element Modeling for Dilatometric Nonisotropy in Steel

It is well known that nonisotropic volume changes in dilatometry were observed during the phase transformation in steel. In this study, a finite element (FE) model incorporating the transformation plasticity was adopted to describe the nonisotropic dilatometric behavior during the phase transformation in steel. An implicit numerical solution procedure to calculate the deformation during the dilatometric experiment was incorporated into the general purpose implicit FE program. The nonisotropic dilatometric behavior could be successfully reproduced by using the FE simulation considering the transformation plasticity. The transformation plasticity was caused by the small amount of stress that naturally developed in the specimen during the dilatometric experiment. In conventional low carbon steel, the stress in the specimen mainly forms due to the very small external force supplied to support it during the dilatometric experiment. As regards ultralow carbon steel, whose phase transformation occurs within an extraordinarily narrow temperature range, the inhomogeneous phase transformation due to the temperature deviation in the specimen was mainly responsible for the stress field in the specimen during the dilatometric experiment.     

Finite-Element Simulation of Conventional and High-Speed Peripheral Milling of Hardened Mold Steel

A finite-element model (FEM) with the flow stress and typical fracture is used to simulate a hard machining process, which before this work could not adequately represent the constitutive behavior of workpiece material that is usually heat treated to hardness levels above 50 Rockwell C hardness (HRC). Thus, a flow stress equation with a variation in hardness is used in the computer simulation of hard machining. In this article, the influence of the milling speed on the cutting force, chip morphology, effective stress, and cutting temperature in the deformation zones of both conventional and high-speed peripheral milling hardened mold steel is systematically studied by finite-element analysis (FEA). By taking into consideration the importance of material characteristics during the milling process, the similar Johnson–Cook’s constitutive equation with hardened mold steel is introduced to the FEM to investigate the peripheral milling of hardened mold steel. In comparison with the experimental data of the cutting force at various cutting speeds, the simulation result is identical with the measured data. The results indicate that the model can be used to accurately predict the behavior of hardened mold steel in both conventional and high-speed milling.     

Finite element simulation of quench hardening

In this study, an efficient finite element model for predicting the temperature field, volume fraction of phases and the evolution of internal stresses up to the residual stress states during quenching of axisymmetrical steel components is developed and implemented. The temperature distribution is determined by considering heat losses to the quenching medium as well as latent heat due to phase transformations. Phase transformations are modelled by discretizing the cooling cuves in a succession of isothermal steps and using the IT-diagrams. For diffusional transformations both Scheil's additivity method and Johnson-Mehl-Avrami equation are used, while Koistinen-Marburger equation is employed for martensitic transformation. Internal stresses are determined by a small strain elasto-plastic analysis using Prandtl-Reuss constitutive equations. Considering long cylinders, a generalized plane strain condition is assumed. The computational model is verified by several experimental measurements and by comparison with other known numerical results. Case studies are performed with St50, Ck45 and C60 type of solid and hollow steel components. The complete data and result sets provided for the verification examples establish a basis for benchmark problems in this field.     

扩散焊接多层材料淬火过程的有限元分析

采用有限元方法模拟了TC4/V/Cu/Ni/GCr15焊后多层材料淬火过程中的温度及应力场,模拟中考虑了轴承钢中马氏体相变的影响.模拟结果表明:淬火过程中,中间层是应力最为集中的区域,钢中发生的马氏体相变起到了降低应力的作用;中间Cu层是剪切应力最为集中的区域;最大剪切应力出现在马氏体相变前铜层外表面处,是引起工件失效的主要原因;轴承钢层厚度的减小可以明显降低工件中最大剪切应力,但不能从根本上消除引起工件失效的危险因素.     

Artificial neural network and finite element modeling of nanoindentation tests

This study first presents two-dimensional (2-D) axisymmetric and three-dimensional (3-D) finite element (FE) models of nanoindentation tests. Calculated load-displacement curves from the FE models are compared with the load-displacement curves from nanoindentation measurements on annealed copper. Numerical parametric studies are also performed to examine the effect of indenter geometry and the material’s stress-strain behavior on the load-displacement response. The 2-D and 3-D FE load-displacement curves compare well with the measured results on annealed copper. The second aspect of this study introduces a new modeling approach for indentation tests using artificial neural networks (ANN). In this approach, ANN models are generated to approximate the FE load-displacement curves for a wide range of material and geometric parameters. The ability of the ANN models to predict the indentation response is examined against other FE results not used as part of the training data. These models are shown to accurately predict the load-displacement behavior of a nonlinear homogeneous material as well as one with a hard film, such as an oxide film, on a relatively soft substrate. It is shown that the monotonic indentation load-displacement response during loading contains ample information for the ANN model to extract material flow properties of the indented material.     

两相区淬火对高强海洋工程钢组织性能的影响

对高强海洋工程用钢分别经过一次淬火+回火(QT)和一次淬火+两相区淬火+回火(QLT)2种热处理工艺处理后,采用扫描电镜(SEM)、连续冷却转变(CCT)曲线、高分辨透射电镜(HRTEM)等手段对其微观组织、相变特性和Cu的析出相进行了检测,并进行了室温拉伸性能及系列温度夏比冲击性能的测定.结果表明:实验钢在0.3～2...     

Composition dependence of young’s modulus in Ti-V, Ti-Nb, and Ti-V-Sn alloys

The Young’s modulus of Ti-V and Ti-V-Sn alloys quenched from the β-phase region after solution treatment and cold rolling was investigated in relation to alloy compositions, microstructures, and constituent phases. The composition dependence of the Young’s modulus for quenched Ti-V binary alloys shows two minima of 69 GPa at Ti-10 mass pct V and 72 GPa at Ti-26 mass pct V. Between the two compositions, athermalω or stress-induced ω is introduced in retainedβ phase and increases Young’s modulus. That is, a low Young’s modulus is attained unless alloys undergoω transformation. In Ti-5 and -8 mass pct V, which under goα′ (hcp) martensitic transformation on quenching, the Young’s modulus further decreases by cold rolling, which can be reasonably explained by the formation ofα′ rolling texture. Comparing Young’s modulus in Ti-V binary alloy with that in Ti-Nb binary alloy, it is found that Young’s modulus is remarkably increased by athermal- or stress inducedω phase, and it shows a minimum when both martensitic andω transformation are suppressed during quenching in metastableβ alloys. The Sn addition to Ti-V binary alloy retards or suppresses athermal and stress-inducedω transformation, thereby decreasing Young’s modulus. Young’s modulus exhibits minimum values of 51 GPa in quenched (Ti-12 pct V)-2 pct Sn and of 57 GPa in cold-rolled (Ti-12 pct V)-6 pct Sn.     

Minimizing the Distortion of Steel Profiles by Controlled Cooling

A complex thermomechanical model is introduced for the simulation of the transient fields of temperature and stresses during the quenching of steel products. The material behaviour is an extension of the classical J₂‐plasticity theory with the extension of temperature and phase fraction dependent yield criteria. The coupling effects, i.e., dissipation of mechanical energy, transformation induced plasticity (TRIP), and phase transformation enthalpy, are considered. The model is used for the determination of the optimal cooling or quenching for reducing the distortion in the long steel profiles. The simulation results are presented in order to investigate the effects of material properties, boundary conditions, profile size and geometry. In the simulations, L‐, T‐ and U‐profiles made of steel C45 and steel C80 are considered. It is demonstrated that with a higher cooling rate in the mass lumped regions of the profiles, the distortion can be reduced.     

Temper Embrittlement Diagram of NiCr Steel Doped with Phosphorus

The temper embrittlement equation of a P-doped NiCr steel and the McLean’s equation for equilibrium intergranular segregation of P in the same steel were derived experimentally. On the basis of these equations, two-dimensional temper embrittlement diagrams were constructed. It was shown that the construction of a temper embrittlement diagram offers a way to predict the ultimate level of temper brittleness of steels.     

Simple model of microsegregation during solidification of steels

A simple analytical model of microsegregation for the solidification of multicomponent steel alloys is presented. This model is based on the Clyne-Kurz model and is extended to take into account the effects of multiple components, a columnar dendrite microstructure, coarsening, and the δ/γ transformation. A new empirical equation to predict secondary dendrite arm spacing as a function of cooling rate and carbon content is presented, based on experimental data measured by several different researchers. The simple microsegregation model is applied to predict phase fractions during solidification, microsegregation of solute elements, and the solidus temperature. The predictions agree well with a range of measured data and the results of a complete finite-difference model. The solidus temperature decreases with either increasing cooling rate or increasing secondary dendrite arm spacing. However, the secondary dendrite arm spacing during solidification decreases with increasing cooling rate. These two opposite effects partly cancel each other, so the solidus temperature does not change much during solidification of a real casting.     

In situ strength evolution during the sintering of bronze powders

Powder metallurgy (PM) allows the fabrication of complex net-shaped components. Accurate design specification of these components requires precise prediction of the compact’s response to sintering process parameters. Nonuniform sintering responses such as strain gradients can result in process failures such as permanent deformation and cracks. To avoid these types of process failures without costly trial-and-error design, the most important response to predict is the compact’s strength as it evolves during the sintering process. A device and method have been developed to characterize the in situ strength evolution as a function of various sintering process parameters. The specific strength parameter investigated and modeled in this article was transverse rupture. This strength was precisely determined for 90Cu-10Sn bronze in response to various combinations of temperature, heating rate, and heating time. The consequence of this work is to identify thermal cycles that minimize distortion and otherwise improve dimensional tolerances.     

Cooling precipitation and strengthening study in powder metallurgy superalloy U720LI

The excellent mechanical properties of powder metallurgy (P/M) superalloys strongly depend on the microstructure, such as grain size, and morphology and size distribution of the γ’ precipitates. The microstructure is, in turn, determined by the heat treatment, viz., solution annealing, quenching, and subsequent aging. To study the effect of the quenching process, two types of quenching methods were used to produce different quenched microstructures in a UDIMET 720LI (U720LI) alloy. One was a continuous quenching method, where samples were colled along linearly controlled cooling profiles, each at a fixed cooling rate. This test studied the effect of cooling rate on the size of cooling γ’ precipitates (formed during quenching) and the consequent strengthening effect. The other test was the interrupted quenching test, which allowed tracking the growth of cooling γ’ precipitates with decreasing temperature during quenching at a given cooling rate. The strengthening response at each interrupt temperature was also studied. Results from the continuous cooling tests showed that the relationship between the size of the cooling γ’ precipitate and the cooling rate obeys a power law, with an exponential being about 0.35. The tensile strength was found to increase linearly with the cooling rate. Strengthening due to the subsequent aging treatment occurred regardless of cooling rates. The interrupted cooling tests showed that γ’ growth is a linear function of decreasing temperature for a given cooling rate. A nonmontonic degradation of tensile strength against interrupt temperature was discovered.     

Continuous cooling transformation diagrams applicable to the heat-affected zone of HSLA-80 and HSLA-100 steels

Continuous cooling transformation (CCT) diagrams for HSLA-80 and HSLA-100 steels pertaining to fusion welding with heat inputs of 10 to 40 kJ/cm, and peak temperatures of 1000 °C to 1400 °C have been developed. The corresponding nonlinear cooling profiles and related γ → α phase transformation start and finish temperatures for various peak temperature conditions have been taken into account. The martensite start (M _s ) temperature for each of the grades and ambient temperature microstructures were considered for mapping the CCT diagrams. The austenite condition and cooling rate are found to influence the phase transformation temperatures, transformation kinetics, and morphology of the transformed products. In the fine-grain heat-affected zone (FGHAZ) of HSLA-80 steel, the transformation during cooling begins at temperatures of 550 °C to 560 °C, and in the HSLA-100 steel at 470 °C to 490 °C. In comparison, the transformation temperature is lower by 120 °C and 30 °C in the coarse-grain heat-affected zone (CGHAZ) of HSLA-80 steel and HSLA-100 steel, respectively. At these temperatures, acicular ferrite (AF) and lath martensite (LM) phases are formed. While the FGHAZ contains a greater proportion of acicular ferrite, the CGHAZ has a higher volume fraction of LM. Cooling profiles from the same peak temperature influence the transformation kinetics with slower cooling rates producing a higher volume fraction of acicular ferrite at the expense of LM. The CCT diagrams produced can predict the microstructure of the entire HAZ and have overcome the limitations of the conventional CCT diagrams, primarily with respect to the CGHAZ.     

退火工艺对Cu-Ni深冲DP钢组织与性能的影响

 为了探讨Cu-Ni合金化深冲双相钢组织性能演变规律,在实验室采用DIL805A/D淬火热膨胀仪与盐浴炉对其连续冷却转变行为及连续退火工艺进行了研究。结果表明,试验钢的Ac1、Ac3分别为821与969 ℃。贝氏体转变冷却速率为0.5~60 ℃/s,铁素体转变冷却速率为0.5~5 ℃/s,冷却速率为3 ℃/s时未发生珠光体转变。在820~880 ℃退火温度范围内试验钢的组织为铁素体与岛状马氏体;随着退火温度的升高,强度与伸长率先减小后增大,而r值呈现先增大后减小的趋势。在880 ℃退火时综合力学性能最佳,屈服强度达401.2 MPa、抗拉强度达451.4 MPa、伸长率为18.6%、r值为1.21。